An object is moving in a circle of radius 100 m with a constant speed of `31.4 m//s` . What is its average speed for one complete revolution

Options

A. Zero
B. `31.4 ms^(-1)`
C. `3.14 ms^(-1)`
D. `sqrt(2)xx31.4 ms^(-1)`

Explanation

To solve the problem of finding the average speed of an object moving in a circle of radius 100 m with a constant speed of 31.4 m/s, we can follow these steps:

### Step 1: Understand the concept of average speed
Average speed is defined as the total distance traveled divided by the total time taken. In the case of circular motion, the object travels a certain distance in one complete revolution.

### Step 2: Calculate the circumference of the circle
The distance traveled in one complete revolution is equal to the circumference of the circle. The formula for the circumference (C) of a circle is given by:
\[ C = 2 \pi r \]
where \( r \) is the radius of the circle.

Given that the radius \( r = 100 \) m, we can calculate the circumference:
\[ C = 2 \pi \times 100 \]
\[ C = 200 \pi \]
Using \( \pi \approx 3.14 \):
\[ C \approx 200 \times 3.14 = 628 \text{ m} \]

### Step 3: Calculate the time taken for one complete revolution
To find the time taken for one complete revolution, we can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Here, the distance is the circumference we just calculated, and the speed is given as 31.4 m/s.

So, the time taken (T) is:
\[ T = \frac{628 \text{ m}}{31.4 \text{ m/s}} \]
Calculating this gives:
\[ T \approx 20 \text{ seconds} \]

### Step 4: Calculate the average speed
Now that we have the total distance traveled (628 m) and the total time taken (20 s), we can calculate the average speed (V_avg):
\[ V_{\text{avg}} = \frac{\text{Total Distance}}{\text{Total Time}} \]
\[ V_{\text{avg}} = \frac{628 \text{ m}}{20 \text{ s}} \]
Calculating this gives:
\[ V_{\text{avg}} = 31.4 \text{ m/s} \]

### Conclusion
The average speed for one complete revolution is **31.4 m/s**.

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